The lower-hybrid drift instability of a plasma driven by relative ion–electron motion is analyzed in the framework of the modified magnetohydrodynamic equations. The Hall contribution is expressed in terms that offer a simple physical interpretation of the process and allow a comprehensive study of various features and limits of instability. It is shown that in the chosen terms there are clear-cut ranges of magnetosonic drift, lower-hybrid drift, and kinetic versions of instability that have different properties. It is shown for the first time that the instability may have, besides a flute-like structure, a cell-like one as well. On the basis of the performed analysis, a new classification of the phenomenon is offered.